We give geometrical conditions, which guarantee the existence of a diffeomorphism in order to transform a nonlinear system without inputs into a canonical normal form depending on its output. Moreover we extend our results to a class of systems with inputs. We end this paper by some examples and its simulations to highlight the proposed algo rithm.

We outline the construction of an algebraic (numerical) representation for Clar's valence formulas which in their geometrical form are illustrated with π-aromatic sextets as inscribed circles in benzenoid rings.

In this paper we consider the Gröbner bases of Grassman algebra and their application to the algebraic geometry. Geometrical statements of constructive type should be given in the coordinate-free form.

We put forward a new model-independent reconstruction scheme for dark energy which utilises the expected geometrical features of the luminosity-distance relation. The important advantage of this scheme is that it does not assume explicit ansatzes for cosmological parameters but only some very general cosmological properties via the geometrical features of the reconstructed luminosity-distance r...

Physical geometry and optical properties of objects are correlated: cylinders focus light to a line, spheres to a point and arbitrarily shaped objects introduce optical aberrations. Multi-functional components with decoupled geometrical form and optical function are needed when specific optical functionalities must be provided while the shapes are dictated by other considerations like ergonomic...

The monopole singularity string, infinite direct line in the rest reference frame, is considered as a rigid physical line, and behavior of its geometrical form under the Lorentz transformations is studied. The method to test the form of any rigid line or surface in relativistical terms is based on the use of light signals emitted from the origin of the reference frame. Influence of the motion o...

In this paper we consider the application of the noncommutative Gröbner bases method for proving theorems in algebraic geometry. Geometrical statements of constructive type should be given in the coordinate-free form. 1. Coordinate-free representation of points and statements We consider theorems of elementary geometry (two-dimensional and three-dimensional). Let A1, A2, A3, . . . , An be point...

In this paper, we present a new approach to geometrical modeling which allows the user to easily characterize and control the shape defined to a closed surface. We will focus on dealing with the shape’s topological, morphological and geometrical properties separately. To do this, we have based our work on the following observations concerning surfaces defined by control-points, and implicit sur...